The following table shows the Myers-Briggs personality preferences for a random

Question

The following table shows the Myers-Briggs personality preferences for a random sample of 519 people in the listed professions. T refers to thinking and F refers to feeling.

Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.01 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H0: Myers-Briggs preference and profession are independent.
H1: Myers-Briggs preference and profession are independent.

H0: Myers-Briggs preference and profession are not independent.
H1: Myers-Briggs preference and profession are not independent.    

H0: Myers-Briggs preference and profession are not independent.
H1: Myers-Briggs preference and profession are independent.

H0: Myers-Briggs preference and profession are independent.
H1: Myers-Briggs preference and profession are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes No     

What sampling distribution will you use?

chi-square

normal     

uniform

binomial

Student's t

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > ?, we fail to reject the null hypothesis.

Since the P-value > ?, we reject the null hypothesis.     

Since the P-value ? ?, we reject the null hypothesis.

Since the P-value ? ?, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 1% level of significance, there is insufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Personality Type Occupation T F Row Total Clergy (all denominations) 56 92 148 M.D. 79 80 159 Lawyer 118 94 212 Column Total 253 266 519

Explanation / Answer

a)

level of significance =0.01
H0: Myers-Briggs preference and profession are independent.
H1: Myers-Briggs preference and profession are not independent.

b)

applying chi square test of independence:

  chi-square statistic =11.161

expected frequencies greater than 5 --Yes

sampling distribution will you use-chi square

degrees of freedom =(row-1)*(column-1)=(3-1)*(2-1)=2

c)

p value =0.004

d)

Since the P-value ? ?, we reject the null hypothesis.

e)

At the 1% level of significance, there is sufficient evidence to conclude that Myers-Briggs preference and the profession are not independent.

Observed OBS T F Total Clergy 56 92 148 MD 79 80 159 Lawyer 118 94 212 Total 253 266 519 Expected Ei=?row*?column/?total T F Total Clergy 72.146 75.854 148 MD 77.509 81.491 159 Lawyer 103.345 108.655 212 Total 253 266 519 chi square =(Oi-Ei)2/Ei T F Total Clergy 3.61 3.44 7.05 MD 0.03 0.027 0.06 Lawyer 2.08 1.977 4.05 Total 5.72 5.44 11.161

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